Existence and global attractivity of periodic solution for a discrete prey–predator model with sex structure

Abstract

In this paper, we investigate the following discrete periodic sex structure model. x 1 ( n + 1 ) = x 1 ( n ) e ( b 1 ( n ) x 2 ( n ) x 1 ( n ) − d 1 ( n ) − k ( n ) x 1 ( n ) − k ( n ) x 2 ( n ) − c 1 ( n ) x 3 ( n ) ) , x 2 ( n + 1 ) = x 2 ( n ) e ( β ( n ) − k ( n ) x 1 ( n ) − k ( n ) x 2 ( n ) − c 1 ( n ) x 3 ( n ) ) , x 3 ( n + 1 ) = x 3 ( n ) e ( − a ( n ) − b ( n ) x 3 ( n ) + c 2 ( n ) x 1 ( n ) + c 2 ( n ) x 2 ( n ) ) . The sufficient and realistic conditions are obtained for the existence and global attractivity of a positive periodic solution for the above system.